Late in the day, I finally made it into the lab... and discovered that things with soft touch power switches had turned themselves on! Most notably for this forum, this included my Rigol DS4000 series scope.
This is configurable in the Utility menu.

I'd say that a device equipped with such "soft" on/off button should NOT power on by itself in case of mains power cycling. Sounds like bad design and not something completely inherent to soft power buttons (but obviously with a simple mechanical switch, it can't happen.)
I agree for certain types of equipment, although for servers in remote locations the automatic power on was a lifesaver. Any power glitches were properly logged and the server gracefully recovered its services.
It could be worse... Keysight's E3631x series of Power supplies have no hard switch - both the fan AND the TFT backlight are turned on permanently! (...)
For real? I had my eye on one of those, but that's definitely a showstopper.
Oh, please keep your eyes on them. They are wonderful power supplies. I couldn't be more pleased.

They solved the mains switch issue decades ago by using pushrods. Shutting down cleanly is a requirement the manufacturers created themselves but which can be solved in other ways.
Yes, the pushrods work really fine, although with the years of use they may develop a screeching sound due to metal-on-metal scrubbing

I have a few that need some fine grease applied, but I just can't get around to do it.
Power switches are critical for embedded OS equipment, as they can allow for the system to perform a proper shutdown. Clunking switches will leave temporary files behind and can cause filesystem corruption. Also, at least on our TV, keeping it on the "sleep" mode allows for a much faster power on (instead of the vaccuum-tube-era power on delay

).